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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">#!/usr/bin/python</span>
<a name="l00002"></a>00002 <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00003"></a>00003 
<a name="l00004"></a>00004 <span class="keyword">from</span> __future__ <span class="keyword">import</span> division
<a name="l00005"></a>00005 
<a name="l00006"></a>00006 <span class="keyword">from</span> math <span class="keyword">import</span> exp, log, sqrt
<a name="l00007"></a>00007 <span class="keyword">from</span> scipy.stats <span class="keyword">import</span> norm
<a name="l00008"></a>00008 <span class="keyword">from</span> scipy <span class="keyword">import</span> isscalar, asarray
<a name="l00009"></a>00009 
<a name="l00010"></a>00010 <span class="keyword">def </span>d_j(j, S, K, r, v, T):
<a name="l00011"></a>00011     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00012"></a>00012 <span class="stringliteral">   d_j = \frac{log(\frac{S}{K})+(r+(-1)^{j-1} \frac{1}{2}v^2)T}{v sqrt(T)}</span>
<a name="l00013"></a>00013 <span class="stringliteral">   &quot;&quot;&quot;</span>
<a name="l00014"></a>00014 
<a name="l00015"></a>00015     <span class="keywordflow">return</span> (log(S / K) + (r + (-1) ** (j - 1) * 0.5 * v * v) * T) / (v
<a name="l00016"></a>00016             * T ** 0.5)
<a name="l00017"></a>00017 
<a name="l00018"></a>00018 <span class="keyword">def </span>vanillaCallPrice(S, K, r, v, T):
<a name="l00019"></a>00019     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00020"></a>00020 <span class="stringliteral">   Price of a European call option struck at K, with spot S,</span>
<a name="l00021"></a>00021 <span class="stringliteral">   constant rate r, constant vol v (over the life of the option)</span>
<a name="l00022"></a>00022 <span class="stringliteral">   and time to maturity T</span>
<a name="l00023"></a>00023 <span class="stringliteral">   &quot;&quot;&quot;</span>
<a name="l00024"></a>00024     <span class="keywordflow">if</span> isscalar(S):
<a name="l00025"></a>00025         <span class="keywordflow">return</span> S * norm.cdf(d_j(1., S, K, r, v, T)) - \
<a name="l00026"></a>00026                K * exp(-r * T) * norm.cdf(d_j(2, S, K, r, v, T))
<a name="l00027"></a>00027     <span class="keywordflow">else</span>:
<a name="l00028"></a>00028         <span class="keywordflow">return</span> asarray([ Si * norm.cdf(d_j(1., Si, K, r, v, T)) - \
<a name="l00029"></a>00029                K * exp(-r * T) * norm.cdf(d_j(2, Si, K, r, v, T)) \
<a name="l00030"></a>00030                <span class="keywordflow">for</span> Si <span class="keywordflow">in</span> S])
<a name="l00031"></a>00031 
<a name="l00032"></a>00032 <span class="keyword">def </span>vanillaPutPrice(S, K, r, v, T):
<a name="l00033"></a>00033     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00034"></a>00034 <span class="stringliteral">     Price of a European put option struck at K, with spot S,</span>
<a name="l00035"></a>00035 <span class="stringliteral">     constant rate r, constant vol v (over the life of the option)</span>
<a name="l00036"></a>00036 <span class="stringliteral">     and time to maturity T</span>
<a name="l00037"></a>00037 <span class="stringliteral">   &quot;&quot;&quot;</span>
<a name="l00038"></a>00038 
<a name="l00039"></a>00039     <span class="keywordflow">if</span> isscalar(S):
<a name="l00040"></a>00040         <span class="keywordflow">return</span> -S * norm.cdf(-d_j( 1, S, K, r, v, T)) + K * exp(-r * T) \
<a name="l00041"></a>00041                    * norm.cdf(-d_j(2, S, K, r, v, T))
<a name="l00042"></a>00042     <span class="keywordflow">else</span>:
<a name="l00043"></a>00043         <span class="keywordflow">return</span> asarray([ -Si * norm.cdf(-d_j( 1, Si, K, r, v, T)) + \
<a name="l00044"></a>00044                 K * exp(-r * T) * norm.cdf(-d_j(2, Si, K, r, v, T)) \
<a name="l00045"></a>00045                 <span class="keywordflow">for</span> Si <span class="keywordflow">in</span> S])
<a name="l00046"></a>00046 
<a name="l00047"></a>00047 <span class="keyword">def </span>vegaVanilla(S, K, r, v, T):
<a name="l00048"></a>00048     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00049"></a>00049 <span class="stringliteral">        Put and Call have the same Vega, Put-Call paraity</span>
<a name="l00050"></a>00050 <span class="stringliteral">    &quot;&quot;&quot;</span>
<a name="l00051"></a>00051     <span class="keywordflow">if</span> isscalar(S):
<a name="l00052"></a>00052         <span class="keywordflow">return</span> S * norm.cdf(d_j( 1, S, K, r, v, T)) * sqrt(T)
<a name="l00053"></a>00053     <span class="keywordflow">else</span>:
<a name="l00054"></a>00054         <span class="keywordflow">return</span> asarray([Si * norm.cdf(d_j( 1, Si, K, r, v, T)) \
<a name="l00055"></a>00055                         <span class="keywordflow">for</span> Si <span class="keywordflow">in</span> S]) * sqrt(T)
<a name="l00056"></a>00056 
<a name="l00057"></a>00057 <span class="comment"># wikipidea</span>
<a name="l00058"></a>00058 <span class="keyword">def </span>cashOrNothingCall(S, K, r, v, T):
<a name="l00059"></a>00059     S = asarray(S)
<a name="l00060"></a>00060     tmp = exp(-r * T) * asarray([norm.cdf(d_j(2, Si, K, r, v, T)) \
<a name="l00061"></a>00061             <span class="keywordflow">for</span> Si <span class="keywordflow">in</span> S], <span class="stringliteral">&#39;float&#39;</span>)
<a name="l00062"></a>00062     <span class="keywordflow">if</span> 1 == S.size:
<a name="l00063"></a>00063         <span class="keywordflow">return</span> float(tmp)
<a name="l00064"></a>00064     <span class="keywordflow">else</span>:
<a name="l00065"></a>00065         <span class="keywordflow">return</span> tmp
<a name="l00066"></a>00066 
<a name="l00067"></a>00067 <span class="keyword">def </span>cashOrNothingPut(S, K, r, v, T):
<a name="l00068"></a>00068     S = asarray(S)
<a name="l00069"></a>00069     tmp = exp(-r * T) * asarray([norm.cdf(-d_j(2, Si, K, r, v, T)) \
<a name="l00070"></a>00070             <span class="keywordflow">for</span> Si <span class="keywordflow">in</span> S], <span class="stringliteral">&#39;float&#39;</span>)
<a name="l00071"></a>00071     <span class="keywordflow">if</span> 1 == S.size:
<a name="l00072"></a>00072         <span class="keywordflow">return</span> float(tmp)
<a name="l00073"></a>00073     <span class="keywordflow">else</span>:
<a name="l00074"></a>00074         <span class="keywordflow">return</span> tmp
<a name="l00075"></a>00075 
<a name="l00076"></a>00076 <span class="keyword">def </span>assetOrNothingCall(S, K, r, q, v, T):
<a name="l00077"></a>00077         <span class="keywordflow">return</span> S * exp( -q * T ) * norm.cdf(d_j(1, S, K, r, v, T))
<a name="l00078"></a>00078 
<a name="l00079"></a>00079 <span class="keyword">def </span>assethOrNothingPut(S, K, r, q, v, T):
<a name="l00080"></a>00080         <span class="keywordflow">return</span> S * exp( -q * T ) * norm.cdf(-d_j(1, S, K, r, v, T))
<a name="l00081"></a>00081 
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